Multi-modal and multi-region distance model for neuroimaging: Application to ABCD study

Large-scale neuroimaging studies often collect multiple modalities, such as task and resting-state functional MRI, diffusion MRI, and structural MRI. Joint inference across these modalities uses shared variation to improve statistical efficiency, increase replicability, and provide a more integrated view of brain-phenotype associations. In practice, however, such analyses are limited because complex cross-modality covariance cannot be flexibly modeled, which makes the resulting joint effects difficult to interpret. A recent distance-based ANOVA extension allows multimodal analysis and increases power for detecting group differences, but it cannot easily distinguish location from scale effects in distance space, offers only an omnibus pseudo-F test without interpretable parameters, and requires computationally intensive permutation inference. We propose a novel semiparametric, U-statistics-based Generalized Estimating Equation (UGEE) framework that unifies univariate and multivariate distance models. By regressing pairwise dissimilarities on covariates, this method yields interpretable regression coefficients that disentangle location and scale effects and quantify inter-modality differences, while flexibly accounting for correlations among modality distances. The estimator is based on efficient influence functions, ensuring asymptotic efficiency, robustness to misspecification, and computational scalability for large-scale data analysis. We evaluate the proposed method through extensive simulations and analyses of the Adolescent Brain Cognitive Development dataset. Results show that UGEE accurately estimates modality, group, and interaction effects and achieves a 100-fold speed-up compared with permutation-based approaches. This framework provides a general and computationally efficient tool for semiparametric inference on multimodal data, particularly suited for large neuroimaging applications.